Stability analysis of dynamic ratcheting in elastoplastic systems

This paper deals with the stability and the dynamics of a harmonically excited elastic perfectly plastic asymmetrical oscillator. The hysteretical system is written as a nonsmooth, forced autonomous system. The dimension of the phase space can be reduced using adapted variables. It is shown that asymmetry of boundary conditions (forcing term) and material asymmetry lead to an equivalent system for this simple structural case. The forced vibration of such an oscillator is treated by a numerical approach by using time locating techniques. Stability of the limit cycles is analytically investigated with a perturbation approach. The boundary between elastoplastic shakedown and dynamic ratcheting is given in closed form. It is shown that the divergence rate is strongly correlated to the internal asymmetry of the oscillator.